My older dd has the same bd as your dd (8/29) and my younger dd's bd is in Sept. We started both of them just as they were about to turn 5. My bd is also in Sept. and I was started at the same age. I would second the thought that it is very individual and the younger kids
do not invariably struggle, as the principal at dds' school tried to convince me.
My older dd is currently in second grade and is working at grade level in some areas and up to 6 grade levels beyond her current grade in others. She and one other girl in her class are very obviously at the top of the class. Both of them have summer birthdays. My younger dd is 12 months or more younger than some of her classmates (a few were held out the extra year). While she is not the "top kid" in the class, she is definitely in the top 1/4 of the class academically. I would anticipate seeing the same pattern that I saw with her older sister as they seem to be pretty developmentally on par -- each year her age has mattered less and less. Her ability is eventually what made the difference.
There has been no social misfit related to them being the youngest either. My little one is a social butterfly and has many friends. She is shorter than the other kids, but she is just destined to be short, poor kiddo! My older dd has some wiring differences and does much better with older children (like 3-5 years older or more). She's not getting that in her current class, but she also wouldn't be getting that if she were grouped with even younger children.
Please do read
this article and
this publication. I hope that one of them has some info that you find helpful. I struggled with this decision, too, and, although we are still in the earlier stages of seeing how it has worked, I am absolutely convinced that it was the right thing for my girls to not wait an extra year. When I look at both of them and imagine them with kids in the younger grade, it just seems like such a huge misfit.